Algebraic Geometry

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Description

Time Mondays, 13.00 - 15.00

Location for Maxwell Institute students: Bayes Centre (room 5.46).

Lecturers: Giulia Gugiatti and Ivan Cheltsov.

Course summary.

Algebraic geometry employs algebraic methods to answer geometric questions. This course offers an introduction to essential concepts, results, and techniques in the field. We will begin with affine varieties and morphisms, then introduce the general notion of variety, and focus on projective varieties. From there, we will study rational maps and blow-ups. Finally, we will define schemes and (quasi-)coherent sheaves.

The main reference will be A. Gathmann's lecture notes.

Other useful references include:  I. Shafarevic, Basic Algebraic Geometry I, II; J. Harris, Algebraic Geometry: A First Course; R. Hartshorne, Algebraic Geometry.

Plan of the lectures.

  • Lecture 1, 06/10. Affine varieties.
  • Lecture 2, 13/10. Zariski topology. 
  • Lecture 3, 20/10. Regular functions and morphisms.
  • Lecture 4, 27/10. Projective varieties.

Tutorials.

We will provide four (possibly five) exercise sheets. There will also be four (possibly five) tutorial sessions led by Joseph Malbon, where you can discuss the exercises. The sessions will take place every other Thursday, starting from October 16, at 11:00 - in the Bayes Centre and streamed online.

Assessments.

There will be two assessments, both designed as group assignments. You are encouraged to collaborate in solving the problems, but each student must submit an individual write-up.

  • Assessment 1: Released on November 3.

  • Assessment 2: Released on December 8.